Well, I think I figured that I could make one of the switches I found work. There are quite a lot of close looking ones on DigiKey and Mouser both. The switch is about 6.5mm by 6mm, thru hole with the snap in solder pins on the outside of the long side spaced about 6.75 mm. The short side of the pins are about 4.5 mm apart. The actuator button is round and somewhat short. Momentary on with a click (tactile). There are four pins but the sets of two on the long side are the same connection. The actual switching is between the short side pins.
It snaps into that plastic grabber frame. The plastic frame seems to be just a spacer. The switch is shown upside down there and actuated by that metal rod with the sort of half round profile as part of it being pushed against the button. I remember now that I was going to remove the switch pcb (unsolder 5 stake pins on the little board) and measure the switch more precisely...especially the actuator button height.
The five stake pins that have to be unsoldered (connections to the main circuit board) are to the right of the picture and not shown.
This is the remote Lionel repaired and there is an almost visible silver dot on the visible side of the switch.